Finite Group DatabasebetaFinite Group Databasebeta| order | 5248 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C41 · Schur multiplier (H2) = C24 |
| direct product | C41×#2010 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C41 | #127 |
| commutator, Frattini, cosocle | C22×C4 | C23×C41 |
| socle | C2×C41 | #392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C41 ◁ C22×C4×C41 ◁ G | |
394 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#7396, C41×#7397, C41×#12114, … |
| maximal normal subgroup of | C41×#7396, C41×#7397, C41×#12114, … |
| maximal quotient of | C41×#9938, C41×#9939, C41×#9940, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5248, 742);